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ric_desc
Riccati equation
Syntax
X=ric_desc(H [,E)) [X1,X2,zero]=ric_desc(H [,E])
Arguments
- H,E
real square matrices
- X1,X2
real square matrices
- zero
real number
Description
Riccati solver with hamiltonian matrices as inputs.
In the continuous time case, the syntax is ric_descr(H)
(one input):
Riccati equation is:
(Ec) A'*X + X*A + X*R*X -Q = 0.
Defining the hamiltonian matrix H
by:
H = [A R; Q -A']
with the syntax [X1,X2,zero]=ric_descr(H)
, the
solution X
is given by X=X1/X2
.
zero
= L1 norm of rhs of (Ec
)
The solution X
is also given by X=riccati(A,Q,R,'c'))
In the discrete-time case, the syntax is ric_descr(H,E)
(two inputs):
The Riccati equation is:
(Ed) A'*X*A-(A'*X*B*(R+B'*X*B)^-1)*(B'*X*A)+C-X = 0.
Defining G=B/R*B'
and the hamiltonian pencil (E,H)
by:
with the syntax [X1,X2,err]=ric_descr(H,E)
, the
solution X
is given by X=X1/X2
.
zero
= L1 norm of rhs of (Ed
)
The solution X
is also given by X=riccati(A,G,C,'d')
with G=B/R*B'
Examples
h=[0.5,4; 0,-0.5] x=ric_desc(h)
See also
- riccati — Riccati equation
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